Formal Approaches in Categorization: Prototype models of categorization: basic formulation, predictions, and limitations

The prototype model has had a long history in cognitive psychology and prototype theory posed an early challenge to the classical view of concepts. Prototype models assume that categories are represented by a summary representation of a category (i.e., a prototype), that might represent information about the most common features, the average feature values, or even the ideal features of a category. Prototype models assume that classification decisions are made on the basis of how similar an object is to a category prototype. This chapter presents a formal description of the model, the motivation and theoretical history of the model, as well as several simulations that illustrate the model’s properties. In general, the prototype model is well-suited to explain the learning of many visual categories (e.g. dot patterns) and categories with a strong family-resemblance structure. Categories are fundamental to cognition, and the ability to learn and use categories is present in all humans and animals. An important theoretical account of categorization is the prototype view (Homa, Cross, Cornell, & Shwartz, 1973; Homa & Cultice, 1984; Minda & Smith, 2001, 2002; Posner & Keele, 1968; J. D. Smith & Minda, 2001; J. D. Smith, Redford, & Haas, 2008; J. D. Smith & Minda, 1998, 2000). The prototype view assumes that a category of things in the world (objects, animals, shapes, etc.) can be represented in the mind by a prototype. A prototype is a cognitive representation that captures the regularities and commonalities among category members and can help a perceiver distinguish category members from non-members. The prototype of a category is often described as the central tendency of the category, as a list of frequently occurring features, or even as an ideal category member. Furthermore, the prototype is similar to category members within the This work was completed with the assistance of a grant from the National Science and Engineering Research Council of Canada (Minda) and grant HD-38051 from the National Institute of Child Health and Human Development (Smith) THE PROTOTYPE MODEL 2 category and less similar (or very dissimilar) to members of other categories. According to the prototype view, objects are classified by first comparing them to the prototypes that are stored in memory, evaluating the similarity evidence from those comparisons, and then classifying the item in accord with the most similar prototype. The prototype view can be realized as a computational model (i.e. the prototype model) that enables a researcher to make specific predictions about the category membership of novel exemplars within a prototype-based framework. The prototype model has been influential in categorization research for several decades as a complementary and balancing perspective to exemplar theory. In this chapter, we present a detailed description of the prototype model (Minda & Smith, 2001; J. D. Smith & Minda, 1998, 2000), we review the historical development of the prototype model, and we present several key predictions of the prototype model. Description of the Model In this section, we provide a basic formulation of how the prototype model calculates similarity and makes a classification decision (Nosofsky, 1992; Minda & Smith, 2001). The formulation of the basic prototype model is closely related to the Generalized Context Model of Nosofsky (Nosofsky, 1986, 1987) which is covered in Chapter 2 of this volume. Of course, the key difference is that to-be-categorized items are compared to prototypes, rather than multiple, specific exemplar traces as in the Context Model. The prototype model makes a classification decision in two steps: comparison and decision. In the comparison phase, a to-be-classified item is compared to the stored prototypes (usually calculated as the modal or average feature values) and the psychological distance between them is converted to a measure of similarity. In the decision phase, the model calculates the probability of the item’s category membership based on the similarity of the item to one prototype divided by the similarity of the item to all the prototypes. The model can be formulated with three equations. First, the distance between the item i and the prototype P is calculated by comparing the two stimuli along each weighted dimension k (see Equation 1).